Calculate the determinint of matrix having -1 and 1 in 1st row and -4 and -1 in 2nd row

The matrix you're referring to is:

\[
\begin{pmatrix}
-1 & 1 \\
-4 & -1
\end{pmatrix}
\]

To calculate the determinant of a 2x2 matrix \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\), use the formula:

\[
\text{Determinant} = (a \cdot d) - (b \cdot c)
\]

Substituting the values:

\[
\text{Determinant} = (-1 \cdot -1) - (1 \cdot -4) = 1 - (-4) = 1 + 4 = 5
\]

So, the determinant of the matrix is **5**.

Would you like any further details or have questions?

Here are 5 related questions:
1. How do you calculate the determinant of a 3x3 matrix?
2. What is the geometric interpretation of a determinant?
3. How does the sign of the determinant affect the orientation of a transformation?
4. Can the determinant of a matrix be zero, and what does it imply?
5. What is Cramer's Rule and how is it related to determinants?

**Tip:** The determinant can also tell you if a matrix is invertible. If the determinant is zero, the matrix is singular and non-invertible.

Calculate the determinant of matrix having -1 and 1 in 1st row and -4 and -1 in 2nd row.

Learn how to calculate the determinant of a 2x2 matrix with values [-1, 1; -4, -1]. This step-by-step guide uses the formula det(A) = (a * d) - (b * c) to find the determinant, covering key linear algebra concepts. Suitable for students in Grades 9-12.

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